Rayleigh length

In optics and especially laser science, the Rayleigh length or Rayleigh range,

, is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled.

[2] The Rayleigh length is particularly important when beams are modeled as Gaussian beams.

For a Gaussian beam propagating in free space along the

axis with wave number

This equation and those that follow assume that the waist is not extraordinarily small;

[3] The radius of the beam at a distance

and the cross sectional area by 2.

The total angular spread of a Gaussian beam in radians is related to the Rayleigh length by[1] The diameter of the beam at its waist (focus spot size) is given by These equations are valid within the limits of the paraxial approximation.

For beams with much larger divergence the Gaussian beam model is no longer accurate and a physical optics analysis is required.